[en] The recently developed coupled-states approximation has been applied to the He--H₂ system for the calculation of the vibrational de-excitation cross sections nj=10→0j' (j'=0,2,4,6,8,10) for energies from threshold up to E) = 0.99 eV. Computations have been carried out for three potential surfaces: (1) Krauss--Mies, (2) Gordon--Secrest, and (3) Gordon--Secrest, modified to include the long-range attraction. The low temperature relaxation rates for each surface are reported and compared to the experimental data from the stimulated Raman technique. V→R energy transfer is found to be very important in the vibrational relaxation process and the modified Gordon--Secrest surface gives the best fit to the experimental data